Taxes and Growth: Theory and Some Back of the Envelope Calculations

Matt Yglesias notes the lack of empirical evidence for a long run tax-growth relationship.

One issue in this neighborhood that I think is interesting is simply the fact that even though it seems like tax policy ought to be an important determinant of economic growth, it’s pretty hard to find evidence for this proposition

I’d only point out that the theoretical evidence is limited as well. First, as surprisingly few people note, theory is ambivalent on the relationship between taxes and work or savings. It is possible that taxes discourage both, but it is equally possible that taxes encourage both.

It depends on whether people stop working or saving because they can’t get much out of it or work and save more because the taxes made them effectively poorer.

Now, it does turn out to be true that its hard to get a model where net private savings goes up when taxes on savings go up. Leaving aside for a moment the fact that all else equal, an increase in taxes produces an increase in public savings, a decrease in private savings still doesn’t portend a long term decrease in the growth rate.

In most models the growth rate declines immediately because there is less investment. However, in time a combination of deprecation of old capital and increases in technology combine to bring the savings and investment rate back to where they were before. What we are left with is an economy that is on a lower growth path, but not a slower growth rate.

One, way to think about it is that is this: suppose we have two countries, one where taxes on savings are high and another where they are low. The two countries will grow together but the low tax country will hit any given level of per capita income a few years earlier than the high tax country. If we assumed that every dollar in tax results in one less dollar of savings and that the low tax country has a tax rate of 20% and the high tax country has a tax rate of 35% then the high tax county will be roughly 12 years behind the low tax country.

The gap between the economies grows in nominal terms but is constant in year terms. That is the second economy is always 12 years behind. This is more clearly displayed on a log chart

Whether this is a big deal or not is a matter of debate. The difference can get quite large. For example for a 50% tax on capital the high tax country is a full 27 years behind. However, in the long run it always reaches the same income per capita as the low tax country, just at a later date.

7 comments

I think you and Yglesias are wrong here. First, there is plenty of empirical evidence that the level of government spending and taxing have an impact on growth, going back, at least, to Barro’s 1991 article in QJE “Economic Growth in a Cross Section of Countries”. Folster and Henrekson (2001) provide more recent and econometrically robust evidence in the European Economic Review, and Peter Gordon and Lanlan Wang in Econ Journal Watch (2004) list several other significant studies as well. This is not to say that the evidence is overwhelming, I would say there is evidence on both sides, but Yglesias is flat out wrong to say “it’s pretty hard to find evidence for this proposition”.

Also, I’m not sure how you contend that it’s a “matter of debate” whether or not a level effect of taxes on GDP is a big deal. What’s the net present value of making everyone in this country 5% poorer than they otherwise would be forever? Well if the economy is around $13 trillion today, thats $650 billion, and with a 6% discount rate that’s over $10 trillion dollars net present value. If that’s not a “big deal” then what is?

My sense for the literature was that studies with longer time horizons tended not to find a strong relationship. One way to look at that is that there are the econometric issues that Folster and Henrekson identify.

Another view, however, is that this supports the notion that countries that transition between higher and lower growth paths when taxes change but that the long run rate does not change.

If we are moving to a 5% lower path over 5 years then that is roughly 0.85% a year knocked off the growth rate, in line with F&H.

As for matter of debate. I think looking at it as a 5% reduction is the most consistent way. Yes, you can get a big present value number but this is because the present value of all future consumption is likewise very large. Over $10T is a big number but it is out of $215T. Its not nearly as big when viewed that way.

Even if your sense of the literature was correct, that is still inconsistent with the claim that it is hard to find evidence that tax policy is unrelated to economic growth. There is counter-evidence to the contrary, yes, but that does not make the evidence for the proposition non-existent.

I’m not a development economist, so you may be correct that the issue may be time horizons, but to me that suggests that the relationship is likely to exist but it is difficult if not impossible to measure at long-horizons due to endogeneity. This is because, as Folster and Henrekson argue, “Over long time spans the level of government spending is likely to be influenced by demographics, in particular an increasing share of elderly.” A higher proportion of elderly population is correlated with a higher GDP because life expectancy increases as we get richer, but an older population means a growing % of GDP goes towards safety nets for the elderly.

As to whether $10T NPV and $650B a year is a big number, I’d venture it is more than the cost of any policy enacted over the last 15 years.

I’m thinking the issue is long run growth. If you transition to a lower path you change short-run growth but the long run growth rate is the same.

And this is a big deal, because a 5% lower path versus a permanent 0.7% lower growth rate will make a huge difference in the out years.

And the point from your email about whether its a big deal as a cost to policy I totally agree with. I don’t think you should just throw 5% of GDP in the ocean.

But we are dealing with the kind of trade-offs that are sensible. Am I willing to have a country that is 5% poorer in exchange for providing a poverty safety net or defeating Al Qaeda. This is the order of magnitude that people are thinking about when that talk causally about the government buying this or that.

If the question is, am I willing to buy these things if it permanently clips my growth rate, then we are talking about something else entirely. Depending on your discount rate you might take very seriously a policy that said taxes and spending should always be as low as possible. If we can maintain order and provide a minimum defense then that is all we should do. The gains in the out years make up for it.

Yeah, but Yglesias’ point isn’t that tax policy effects the level of GDP and that’s important, but the stuff we’re spending the money on is really really important. His point is that there is no evidence that taxes affect growth rates, and growth rates are all that really matters. He’s wrong on both points, and I don’t think you’ve yet disagreed with me on that.

You can argue about the econometrics or the different possible implications of the time horizon of the sample, but you cannot say there is no evidence.

I also don’t think you’ve disagreed that depending on relative size of the level effect and the growth effect and our discount rate, we might prefer a decrease in growth versus over a decrease in level. This is especially true over the only time period he specifically refers to, which is “several decades”. And so it’s wrong to point to the supposed lack of impact on taxes on growth and say “therefore it doesn’t really matter”.